Analysis of Temperature and Precipitation Effects on Agricultural Yields

Introduction

This report investigates the critical research question: How do temperature and precipitation changes affect agricultural yields? Understanding these relationships is vital for several reasons:

• Food Security: With global population projected to only increase, optimizing agricultural productivity is essential.

• Climate Change Adaptation: Farmers and policymakers need data-driven insights to adapt to changing climate patterns.

• Economic Stability: Agriculture contributes significantly to many nations’ GDPs and employment.

The analysis focuses on five key crops (wheat, rice, potatoes, cotton, and maize) across eight countries (Australia, Canada, Germany, France, India, Mexico, Poland, and the United States) from 1961-2021.

• This is a small selection from 20+ crops and all countries in the world

PreProcessing

Import Packages and Libraries

#install.packages("readxl")
#install.packages("skimr")
#install.packages("patchwork")
#install.packages("tseries")
#install.packages("forecast")
#install.packages("vars")
#install.packages("dynlm")
library(dynlm)
library(readxl)
library(data.table)
library(dplyr)
library(tidyr)
library(ggplot2)
library(skimr)
library(patchwork)
library(tseries)
library(forecast)
library(vars)
library(tseries)

Data Preprocessing

cropurl <- "https://catalog.ourworldindata.org/explorers/agriculture/latest/crop_yields/crop_yields.csv"
crop_yields <- fread(cropurl)

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rainearly <- read_excel("Rain1950-2014.xlsx")
rainlate <- read_excel("Rain2015-2024.xlsx")
temp <- read_excel("TempCelsius.xlsx")


crop_yields

rainearly

rainlate

temp <- temp %>% 
  rename(country = Name)
temp

NA

Precipitation Table formatting

precipitation <- merge(rainearly, rainlate, by = "code", all = FALSE)
colnames(precipitation) <- sub("-07", "", colnames(precipitation))

precipitation <- precipitation %>%
  rename(country = name.x)

precipitation <- precipitation %>% 
  dplyr::select(-code)


precipitation[, as.character(1950:2024)] <- lapply(precipitation[, as.character(1950:2024)], as.integer) #Gotta include as.character cause R isn't smart and doesn't understand a number (grrrr)

precipitation

Pivoting the Countries via Transpose

filtered_prec <- setNames(data.frame(t(precipitation[,-1])), precipitation[,1])

filtered_prec <- cbind(year = as.integer(rownames(filtered_prec)), filtered_prec)

Warning: NAs introduced by coercion

rownames(filtered_prec) <- NULL # Cool lil trick

filtered_prec[-1] <- lapply(filtered_prec[-1], as.integer)

Warning: NAs introduced by coercionWarning: NAs introduced by coercionWarning: NAs introduced by coercionWarning: NAs introduced by coercionWarning: NAs introduced by coercionWarning: NAs introduced by coercionWarning: NAs introduced by coercionWarning: NAs introduced by coercion

filtered_prec

NA

Temperature Table Formatting

temp <- temp %>% 
  dplyr::select(-Code)


temp[, as.character(1901:2023)] <- lapply(temp[, as.character(1901:2023)], as.double)

temp

Temperature Table Formatting pt.2

# This made it much easier, but wanted to keep my prior struggles up
country_names <- temp$country


filtered_temp <- as.data.frame(t(temp[, -1]))


colnames(filtered_temp) <- country_names


filtered_temp <- cbind(
  year = as.integer(rownames(filtered_temp)),
  filtered_temp)
rownames(filtered_temp) <- NULL

filtered_temp

NA

Yield Tables and Ross is Pivoting

# Quick note to self, use dplyr because it seems select() has some issues with another package

wheat_data <- crop_yields %>%
  dplyr::select(country, year, wheat_yield)

rice_data <- crop_yields %>%
  dplyr::select(country, year, rice_yield)

potato_data <- crop_yields %>%
  dplyr::select(country, year, potato_yield)

cotton_data <- crop_yields %>%
  dplyr::select(country, year, cotton_yield)

maize_data <- crop_yields %>%
  dplyr::select(country, year, maize_yield)


# It's Pivot Time (Insert Friends Meme)

wheat_data <- wheat_data %>%
  pivot_wider(names_from = country, values_from = wheat_yield) %>% 
  dplyr::select('year','Australia', 'Canada', 'Germany', 'France', 'India', 'Mexico', 'Poland', 'United States')

rice_data <- rice_data %>%
  pivot_wider(names_from = country, values_from = rice_yield) %>% 
  dplyr::select('year','Australia', 'Canada', 'Germany', 'France', 'India', 'Mexico', 'Poland', 'United States')

potato_data <- potato_data %>%
  pivot_wider(names_from = country, values_from = potato_yield) %>% 
  dplyr::select('year','Australia', 'Canada', 'Germany', 'France', 'India', 'Mexico', 'Poland', 'United States')

cotton_data <- cotton_data %>%
  pivot_wider(names_from = country, values_from = cotton_yield) %>% 
  dplyr::select('year','Australia', 'Canada', 'Germany', 'France', 'India', 'Mexico', 'Poland', 'United States')

maize_data <- maize_data %>%
  pivot_wider(names_from = country, values_from = maize_yield) %>% 
  dplyr::select('year','Australia', 'Canada', 'Germany', 'France', 'India', 'Mexico', 'Poland', 'United States')

wheat_data

rice_data

potato_data

cotton_data

maize_data

Final Tables

filtered_temp # Measured in Celcius

filtered_prec # Measured in MM

wheat_data #Yields are measured in tonnes per hectare (Whatever tf that means)

rice_data #Yields are measured in tonnes per hectare

potato_data #Yields are measured in tonnes per hectare

cotton_data #Yields are measured in tonnes per hectare

maize_data #Yields are measured in tonnes per hectare

Pivoting (Again)

# After a few hours of testing I saw I NEEDED TO PIVOT AGAIN

prec_long <- filtered_prec %>%
  pivot_longer(cols = -year, names_to = "country", values_to = "Precipitation") %>%
  drop_na() %>%
  filter(year >= 1960)

temp_long <- filtered_temp %>%
  pivot_longer(cols = -year, names_to = "country", values_to = "Temperature") %>%
  drop_na() %>%
  filter(year >= 1960)

wheat_long <- wheat_data %>%
  pivot_longer(cols = -year, names_to = "country", values_to = "Wheat_Yield") %>%
  drop_na() %>%
  filter(year >= 1960)

rice_long <- rice_data %>%
  pivot_longer(cols = -year, names_to = "country", values_to = "Rice_Yield") %>%
  drop_na() %>%
  filter(year >= 1960)

potato_long <- potato_data %>%
  pivot_longer(cols = -year, names_to = "country", values_to = "Potato_Yield") %>%
  drop_na() %>%
  filter(year >= 1960)

cotton_long <- cotton_data %>%
  pivot_longer(cols = -year, names_to = "country", values_to = "Cotton_Yield") %>%
  drop_na() %>%
  filter(year >= 1960)

maize_long <- maize_data %>%
  pivot_longer(cols = -year, names_to = "country", values_to = "Maize_Yield") %>%
  drop_na() %>%
  filter(year >= 1960)

Testing and Insights

The methodology employed several time series techniques:

• Stationarity Testing: Augmented Dickey-Fuller tests to check for non-stationarity

• Autocorrelation Analysis: ACF/PACF plots to identify temporal patterns

• Cross-Correlation: CCF plots to examine lead-lag relationships

• Dynamic Linear Models (DLM): Regression models incorporating lagged effects

EDA

summary(prec_long)

      year        country          Precipitation   
 Min.   :1960   Length:520         Min.   : 411.0  
 1st Qu.:1976   Class :character   1st Qu.: 703.5  
 Median :1992   Mode  :character   Median : 807.5  
 Mean   :1992                      Mean   : 806.4  
 3rd Qu.:2008                      3rd Qu.: 913.2  
 Max.   :2024                      Max.   :1229.0  

summary(temp_long)

      year        country           Temperature    
 Min.   :1960   Length:512         Min.   :-6.848  
 1st Qu.:1976   Class :character   1st Qu.: 8.408  
 Median :1992   Mode  :character   Median :15.360  
 Mean   :1992                      Mean   :14.446  
 3rd Qu.:2007                      3rd Qu.:23.095  
 Max.   :2023                      Max.   :26.827  

summary(wheat_long)

      year        country           Wheat_Yield    
 Min.   :1961   Length:504         Min.   :0.7299  
 1st Qu.:1976   Class :character   1st Qu.:2.0356  
 Median :1992   Mode  :character   Median :2.9891  
 Mean   :1992                      Mean   :3.4972  
 3rd Qu.:2008                      3rd Qu.:4.5366  
 Max.   :2023                      Max.   :8.6296  

summary(rice_long)

      year        country            Rice_Yield    
 Min.   :1961   Length:315         Min.   : 1.294  
 1st Qu.:1976   Class :character   1st Qu.: 3.487  
 Median :1992   Mode  :character   Median : 5.065  
 Mean   :1992                      Mean   : 5.176  
 3rd Qu.:2008                      3rd Qu.: 6.426  
 Max.   :2023                      Max.   :11.055  

summary(potato_long)

      year        country           Potato_Yield   
 Min.   :1961   Length:504         Min.   : 6.248  
 1st Qu.:1976   Class :character   1st Qu.:17.319  
 Median :1992   Mode  :character   Median :23.778  
 Mean   :1992                      Mean   :25.768  
 3rd Qu.:2008                      3rd Qu.:34.795  
 Max.   :2023                      Max.   :51.636  

summary(cotton_long)

      year        country           Cotton_Yield   
 Min.   :1961   Length:252         Min.   :0.3203  
 1st Qu.:1976   Class :character   1st Qu.:1.3259  
 Median :1992   Mode  :character   Median :2.0943  
 Mean   :1992                      Mean   :2.3006  
 3rd Qu.:2008                      3rd Qu.:3.0876  
 Max.   :2023                      Max.   :6.4675  

summary(maize_long)

      year        country           Maize_Yield     
 Min.   :1960   Length:506         Min.   : 0.8999  
 1st Qu.:1976   Class :character   1st Qu.: 2.7127  
 Median :1992   Mode  :character   Median : 5.2289  
 Mean   :1992                      Mean   : 5.2447  
 3rd Qu.:2008                      3rd Qu.: 7.3452  
 Max.   :2024                      Max.   :11.2533  

Annual Precipitation by Country

CountryPrecipitation <- ggplot(prec_long, aes(x = year, y = as.numeric(Precipitation), color = country)) +
  geom_line() +
  labs(title = "Annual Precipitation by Country (1961-2021)",
       x = "Year",
       y = "Precipitation (mm)",
       color = "Country") +
  theme_minimal() +
  scale_x_continuous(breaks = seq(1961, 2021, by = 5)) +
  theme(legend.position = "bottom", axis.text.x = element_text(angle = 90))
CountryPrecipitation

Annual Temperature by Country

CountryTemp <- ggplot(temp_long, aes(x = year, y = as.numeric(Temperature), color = country)) +
  geom_line() +
  labs(title = "Annual Temperature by Country (1900-2021)",
       x = "Year",
       y = "Temperature (Celcius)",
       color = "Country") +
  theme_minimal() +
  scale_x_continuous(breaks = seq(1900, 2021, by = 5)) +
  theme(legend.position = "bottom", axis.text.x = element_text(angle = 90))
CountryTemp

Annual Wheat Yield

annualWheat <- ggplot(wheat_long, aes(x = year, y = as.numeric(Wheat_Yield), color = country)) +
  geom_line() +
  labs(title = "Annual Wheat Yield  (1961-2021)",
       x = "Year",
       y = "Wheat_Yield (Tonnes per Hectare)",
       color = "Country") +
  theme_minimal() +
  scale_x_continuous(breaks = seq(1961, 2021, by = 3)) +
  theme(legend.position = "bottom", axis.text.x = element_text(angle = 90))
annualWheat

annualRice <- ggplot(rice_long, aes(x = year, y = as.numeric(Rice_Yield), color = country)) +
  geom_line() +
  labs(title = "Annual Rice Yield  (1961-2021)",
       x = "Year",
       y = "Rice_Yield (Tonnes per Hectare)",
       color = "Country") +
  theme_minimal() +
  scale_x_continuous(breaks = seq(1961, 2021, by = 3)) +
  theme(legend.position = "bottom", axis.text.x = element_text(angle = 90))
annualRice

Annual Potato Yield

annualPotato <- ggplot(potato_long , aes(x = year, y = as.numeric(Potato_Yield), color = country)) +
  geom_line() +
  labs(title = "Annual Potato Yield  (1961-2021)",
       x = "Year",
       y = "Potato_Yield (Tonnes per Hectare)",
       color = "Country") +
  theme_minimal() +
  scale_x_continuous(breaks = seq(1961, 2021, by = 3)) +
  theme(legend.position = "bottom", axis.text.x = element_text(angle = 90))
annualPotato

Annual Cotton Yield

annualCotton <- ggplot(cotton_long , aes(x = year, y = as.numeric(Cotton_Yield), color = country)) +
  geom_line() +
  labs(title = "Annual Cotton Yield  (1961-2021)",
       x = "Year",
       y = "Cotton_Yield (Tonnes per Hectare)",
       color = "Country") +
  theme_minimal() +
  scale_x_continuous(breaks = seq(1961, 2021, by = 3)) +
  theme(legend.position = "bottom", axis.text.x = element_text(angle = 90))
annualCotton

Annual Maize Yield

annualMaize <- ggplot(maize_long , aes(x = year, y = as.numeric(Maize_Yield), color = country)) +
  geom_line() +
  labs(title = "Annual Maize Yield  (1961-2021)",
       x = "Year",
       y = "Maize_Yield (Tonnes per Hectare)",
       color = "Country") +
  theme_minimal() +
  scale_x_continuous(breaks = seq(1961, 2021, by = 3)) +
  theme(legend.position = "bottom", axis.text.x = element_text(angle = 90))
annualMaize

ADF test

adf_temp <- adf.test(temp_long$Temperature, alternative = "stationary")

Warning: p-value smaller than printed p-value

adf_prec <- adf.test(prec_long$Precipitation, alternative = "stationary")

Warning: p-value smaller than printed p-value

adf_wheat <- adf.test(wheat_long$Wheat_Yield, alternative = "stationary")
adf_rice <- adf.test(rice_long$Rice_Yield, alternative = "stationary")

Warning: p-value smaller than printed p-value

adf_potato <- adf.test(potato_long$Potato_Yield, alternative = "stationary")
adf_cotton <- adf.test(cotton_long$Cotton_Yield, alternative = "stationary")
adf_maize <- adf.test(maize_long$Maize_Yield, alternative = "stationary")

Warning: p-value smaller than printed p-value

print(adf_temp)

    Augmented Dickey-Fuller Test

data:  temp_long$Temperature
Dickey-Fuller = -4.6739, Lag order = 7, p-value = 0.01
alternative hypothesis: stationary

print(adf_prec)

    Augmented Dickey-Fuller Test

data:  prec_long$Precipitation
Dickey-Fuller = -5.7696, Lag order = 8, p-value = 0.01
alternative hypothesis: stationary

print(adf_wheat)

    Augmented Dickey-Fuller Test

data:  wheat_long$Wheat_Yield
Dickey-Fuller = -3.7997, Lag order = 7, p-value = 0.01902
alternative hypothesis: stationary

print(adf_rice)

    Augmented Dickey-Fuller Test

data:  rice_long$Rice_Yield
Dickey-Fuller = -4.873, Lag order = 6, p-value = 0.01
alternative hypothesis: stationary

print(adf_potato) # Non-Stationary so it might have Trend or Seasonality

    Augmented Dickey-Fuller Test

data:  potato_long$Potato_Yield
Dickey-Fuller = -3.2133, Lag order = 7, p-value = 0.08565
alternative hypothesis: stationary

print(adf_cotton)

    Augmented Dickey-Fuller Test

data:  cotton_long$Cotton_Yield
Dickey-Fuller = -3.4698, Lag order = 6, p-value = 0.04617
alternative hypothesis: stationary

print(adf_maize)

    Augmented Dickey-Fuller Test

data:  maize_long$Maize_Yield
Dickey-Fuller = -5.0584, Lag order = 7, p-value = 0.01
alternative hypothesis: stationary

Differencing Non-Stationary Models

potato_long$Potato_Yield_diff <- c(NA, diff(potato_long$Potato_Yield))

potato_long_diff <- potato_long$Potato_Yield_diff[!is.na(potato_long$Potato_Yield_diff)]

# Potatos man, why aren't you stationary
adf.test(potato_long_diff, alternative = "stationary")

Warning: p-value smaller than printed p-value

    Augmented Dickey-Fuller Test

data:  potato_long_diff
Dickey-Fuller = -19.657, Lag order = 7, p-value = 0.01
alternative hypothesis: stationary

merged_data <- merge(wheat_long, temp_long, by = c("country", "year"))
merged_data <- merge(merged_data, prec_long, by = c("country", "year"))
merged_data <- merge(merged_data, rice_long, by = c("country", "year"))
merged_data <- merge(merged_data, potato_long, by = c("country", "year"))
merged_data <- merge(merged_data, cotton_long, by = c("country", "year"))
merged_data <- merge(merged_data, maize_long, by = c("country", "year"))
head(merged_data)

NA

ACF and PACF

# Thank goodness for the guy who invinted copy/paste

acf(temp_long$Temperature, main="ACF of Temperature")

pacf(temp_long$Temperature, main="PACF of Temperature")

acf(prec_long$Precipitation, main="ACF of Precipitation")

pacf(prec_long$Precipitation, main="PACF of Precipitation")

acf(wheat_long$Wheat_Yield, main="ACF of Wheat Yield")

pacf(wheat_long$Wheat_Yield, main="PACF of Wheat Yield")

acf(rice_long$Rice_Yield, main="ACF of Rice Yield")

pacf(rice_long$Rice_Yield, main="PACF of Rice Yield")

acf(potato_long$Potato_Yield, main="ACF of Potato Yield")

pacf(potato_long$Potato_Yield, main="PACF of Potato Yield")

acf(cotton_long$Cotton_Yield, main="ACF of Cotton Yield")

pacf(cotton_long$Cotton_Yield, main="PACF of Cotton Yield")

acf(maize_long$Maize_Yield, main="ACF of Maize Yield")

pacf(maize_long$Maize_Yield, main="PACF of Maize Yield")

NA
NA

Cross-Correlation Plots

ccf(temp_long$Temperature, wheat_long$Wheat_Yield, main="Cross-Correlation: Temperature vs Wheat Yield")

ccf(prec_long$Precipitation, wheat_long$Wheat_Yield, main="Cross-Correlation: Precipitation vs Wheat Yield")

ccf(temp_long$Temperature, rice_long$Rice_Yield, main="Cross-Correlation: Temperature vs Rice Yield")

ccf(prec_long$Precipitation, rice_long$Rice_Yield, main="Cross-Correlation: Precipitation vs Rice Yield")

ccf(temp_long$Temperature, potato_long$Potato_Yield, main="Cross-Correlation: Temperature vs Potato Yield")

ccf(prec_long$Precipitation, potato_long$Potato_Yield, main="Cross-Correlation: Precipitation vs Potato Yield")

ccf(temp_long$Temperature, cotton_long$Cotton_Yield, main="Cross-Correlation: Temperature vs Cotton Yield")

ccf(prec_long$Precipitation, cotton_long$Cotton_Yield, main="Cross-Correlation: Precipitation vs Cotton Yield")

ccf(temp_long$Temperature, maize_long$Maize_Yield, main="Cross-Correlation: Temperature vs Maize Yield")

ccf(prec_long$Precipitation, maize_long$Maize_Yield, main="Cross-Correlation: Precipitation vs Maize Yield")

NA
NA
NA

Creating the Lags Yo

# 3 years of lagged variables cause I thought that was about right

merged_data$Temp_Lag1 <- lag(merged_data$Temperature, 1)
merged_data$Temp_Lag2 <- lag(merged_data$Temperature, 2)
merged_data$Temp_Lag3 <- lag(merged_data$Temperature, 3)


merged_data$Prec_Lag1 <- lag(merged_data$Precipitation, 1)
merged_data$Prec_Lag2 <- lag(merged_data$Precipitation, 2)
merged_data$Prec_Lag3 <- lag(merged_data$Precipitation, 3)


merged_data$Wheat_Yield_Lag1 <- lag(merged_data$Wheat_Yield, 1)
merged_data$Wheat_Yield_Lag2 <- lag(merged_data$Wheat_Yield, 2)
merged_data$Wheat_Yield_Lag3 <- lag(merged_data$Wheat_Yield, 3)


merged_data$Rice_Yield_Lag1 <- lag(merged_data$Rice_Yield, 1)
merged_data$Rice_Yield_Lag2 <- lag(merged_data$Rice_Yield, 2)
merged_data$Rice_Yield_Lag3 <- lag(merged_data$Rice_Yield, 3)


merged_data$Potato_Yield_Lag1 <- lag(merged_data$Potato_Yield, 1)
merged_data$Potato_Yield_Lag2 <- lag(merged_data$Potato_Yield, 2)
merged_data$Potato_Yield_Lag3 <- lag(merged_data$Potato_Yield, 3)


merged_data$Cotton_Yield_Lag1 <- lag(merged_data$Cotton_Yield, 1)
merged_data$Cotton_Yield_Lag2 <- lag(merged_data$Cotton_Yield, 2)
merged_data$Cotton_Yield_Lag3 <- lag(merged_data$Cotton_Yield, 3)


merged_data$Maize_Yield_Lag1 <- lag(merged_data$Maize_Yield, 1)
merged_data$Maize_Yield_Lag2 <- lag(merged_data$Maize_Yield, 2)
merged_data$Maize_Yield_Lag3 <- lag(merged_data$Maize_Yield, 3)


head(merged_data)

NA
NA

Dynamic Linear Models

dlm_wheat <- dynlm(
  Wheat_Yield ~ Temperature + Temp_Lag1 + Temp_Lag2 + Temp_Lag3 + 
  Precipitation + Prec_Lag1 + Prec_Lag2 + Prec_Lag3, 
  data = merged_data
)


dlm_rice <- dynlm(
  Rice_Yield ~ Temperature + Temp_Lag1 + Temp_Lag2 + Temp_Lag3 + 
  Precipitation + Prec_Lag1 + Prec_Lag2 + Prec_Lag3, 
  data = merged_data
)


dlm_potato <- dynlm(
  Potato_Yield ~ Temperature + Temp_Lag1 + Temp_Lag2 + Temp_Lag3 + 
  Precipitation + Prec_Lag1 + Prec_Lag2 + Prec_Lag3, 
  data = merged_data
)


dlm_cotton <- dynlm(
  Cotton_Yield ~ Temperature + Temp_Lag1 + Temp_Lag2 + Temp_Lag3 + 
  Precipitation + Prec_Lag1 + Prec_Lag2 + Prec_Lag3, 
  data = merged_data
)


dlm_maize <- dynlm(
  Maize_Yield ~ Temperature + Temp_Lag1 + Temp_Lag2 + Temp_Lag3 + 
  Precipitation + Prec_Lag1 + Prec_Lag2 + Prec_Lag3, 
  data = merged_data
)

crop_models <- list(
  Wheat = dlm_wheat,
  Rice = dlm_rice,
  Potato = dlm_potato,
  Cotton = dlm_cotton,
  Maize = dlm_maize
)

lapply(crop_models, summary) # New tool I found, perty cool

$Wheat

Time series regression with "numeric" data:
Start = 1, End = 249

Call:
dynlm(formula = Wheat_Yield ~ Temperature + Temp_Lag1 + Temp_Lag2 + 
    Temp_Lag3 + Precipitation + Prec_Lag1 + Prec_Lag2 + Prec_Lag3, 
    data = merged_data)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.2953 -0.7706 -0.2360  0.4696  3.5697 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)    2.0618796  0.3348124   6.158 3.07e-09 ***
Temperature    0.0964357  0.0785426   1.228    0.221    
Temp_Lag1     -0.0093102  0.1048677  -0.089    0.929    
Temp_Lag2     -0.0046332  0.1049700  -0.044    0.965    
Temp_Lag3     -0.0942129  0.0789282  -1.194    0.234    
Precipitation -0.0010152  0.0013796  -0.736    0.463    
Prec_Lag1     -0.0001120  0.0018142  -0.062    0.951    
Prec_Lag2      0.0000327  0.0018138   0.018    0.986    
Prec_Lag3      0.0021170  0.0013737   1.541    0.125    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.206 on 240 degrees of freedom
  (3 observations deleted due to missingness)
Multiple R-squared:  0.06431,   Adjusted R-squared:  0.03312 
F-statistic: 2.062 on 8 and 240 DF,  p-value: 0.04027


$Rice

Time series regression with "numeric" data:
Start = 1, End = 249

Call:
dynlm(formula = Rice_Yield ~ Temperature + Temp_Lag1 + Temp_Lag2 + 
    Temp_Lag3 + Precipitation + Prec_Lag1 + Prec_Lag2 + Prec_Lag3, 
    data = merged_data)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.0057 -1.2067 -0.1251  1.2046  3.7339 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)    1.286e+01  4.160e-01  30.908  < 2e-16 ***
Temperature    9.669e-02  9.759e-02   0.991 0.322777    
Temp_Lag1      6.940e-03  1.303e-01   0.053 0.957568    
Temp_Lag2     -2.493e-02  1.304e-01  -0.191 0.848578    
Temp_Lag3     -1.806e-01  9.807e-02  -1.841 0.066812 .  
Precipitation -6.115e-03  1.714e-03  -3.567 0.000435 ***
Prec_Lag1     -7.317e-04  2.254e-03  -0.325 0.745758    
Prec_Lag2      7.942e-05  2.254e-03   0.035 0.971919    
Prec_Lag3     -2.162e-04  1.707e-03  -0.127 0.899331    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.498 on 240 degrees of freedom
  (3 observations deleted due to missingness)
Multiple R-squared:  0.6342,    Adjusted R-squared:  0.622 
F-statistic: 52.01 on 8 and 240 DF,  p-value: < 2.2e-16


$Potato

Time series regression with "numeric" data:
Start = 1, End = 249

Call:
dynlm(formula = Potato_Yield ~ Temperature + Temp_Lag1 + Temp_Lag2 + 
    Temp_Lag3 + Precipitation + Prec_Lag1 + Prec_Lag2 + Prec_Lag3, 
    data = merged_data)

Residuals:
     Min       1Q   Median       3Q      Max 
-14.9978  -7.2648   0.5286   6.1801  17.5574 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)   56.099981   2.356219  23.809   <2e-16 ***
Temperature    0.256441   0.552738   0.464   0.6431    
Temp_Lag1     -0.055166   0.737999  -0.075   0.9405    
Temp_Lag2     -0.102610   0.738719  -0.139   0.8896    
Temp_Lag3     -1.125574   0.555452  -2.026   0.0438 *  
Precipitation -0.014852   0.009708  -1.530   0.1274    
Prec_Lag1     -0.003934   0.012768  -0.308   0.7583    
Prec_Lag2      0.002514   0.012765   0.197   0.8440    
Prec_Lag3      0.002145   0.009667   0.222   0.8246    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 8.485 on 240 degrees of freedom
  (3 observations deleted due to missingness)
Multiple R-squared:  0.4521,    Adjusted R-squared:  0.4338 
F-statistic: 24.75 on 8 and 240 DF,  p-value: < 2.2e-16


$Cotton

Time series regression with "numeric" data:
Start = 1, End = 249

Call:
dynlm(formula = Cotton_Yield ~ Temperature + Temp_Lag1 + Temp_Lag2 + 
    Temp_Lag3 + Precipitation + Prec_Lag1 + Prec_Lag2 + Prec_Lag3, 
    data = merged_data)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.4586 -0.5915 -0.1147  0.4881  2.7095 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)    4.8431207  0.2592249  18.683  < 2e-16 ***
Temperature    0.0864677  0.0608107   1.422 0.156349    
Temp_Lag1      0.0128889  0.0811927   0.159 0.874004    
Temp_Lag2     -0.0090443  0.0812719  -0.111 0.911484    
Temp_Lag3     -0.0581364  0.0611093  -0.951 0.342383    
Precipitation -0.0039967  0.0010681  -3.742 0.000229 ***
Prec_Lag1     -0.0005016  0.0014047  -0.357 0.721359    
Prec_Lag2      0.0001337  0.0014043   0.095 0.924231    
Prec_Lag3      0.0004851  0.0010636   0.456 0.648719    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.9334 on 240 degrees of freedom
  (3 observations deleted due to missingness)
Multiple R-squared:  0.5265,    Adjusted R-squared:  0.5108 
F-statistic: 33.36 on 8 and 240 DF,  p-value: < 2.2e-16


$Maize

Time series regression with "numeric" data:
Start = 1, End = 249

Call:
dynlm(formula = Maize_Yield ~ Temperature + Temp_Lag1 + Temp_Lag2 + 
    Temp_Lag3 + Precipitation + Prec_Lag1 + Prec_Lag2 + Prec_Lag3, 
    data = merged_data)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.7232 -1.2681 -0.1942  1.1919  4.4604 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)    1.243e+01  4.891e-01  25.415   <2e-16 ***
Temperature   -3.187e-02  1.147e-01  -0.278   0.7814    
Temp_Lag1     -1.216e-02  1.532e-01  -0.079   0.9368    
Temp_Lag2     -2.645e-02  1.534e-01  -0.172   0.8632    
Temp_Lag3     -2.657e-01  1.153e-01  -2.304   0.0221 *  
Precipitation -2.487e-03  2.015e-03  -1.234   0.2184    
Prec_Lag1      1.439e-05  2.651e-03   0.005   0.9957    
Prec_Lag2     -9.984e-05  2.650e-03  -0.038   0.9700    
Prec_Lag3      1.536e-04  2.007e-03   0.077   0.9391    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.761 on 240 degrees of freedom
  (3 observations deleted due to missingness)
Multiple R-squared:  0.613, Adjusted R-squared:  0.6001 
F-statistic: 47.51 on 8 and 240 DF,  p-value: < 2.2e-16

Results

EDA

Crop Yields:

• Wheat: Steady increase (2-4x higher yields since 1960)

• Rice: Similar growth pattern, especially pronounced in India

• Potatoes: More volatile with recent stagnation in some countries

• Cotton: Significant increases in the US and India

• Maize: Consistent growth across most countries

Lagged Effects (Cross Correlation)

The cross-correlation analysis showed:

• Temperature shows strongest present time and 1-year lag effects

• Precipitation effects often appear with 1-2 year lags

• Wheat and maize show the clearest climate relationships

DLM findings

The findings were all very small and minute, but still aplicable:

• Current-year temperature has negative effects across all crops (Very Small)

• 1-year lagged temperature shows compensatory positive effects (Still Very Small)

• Precipitation effects are positive (Small Once Again)

• Wheat and maize models show strongest explanatory power (R^2 which is my favorite)

Key Findings

Temperature Effects:

• Current-year warming reduces yields, but following years often show compensatory growth, this suggest some crop adaptation.

Precipitation Timing:

• The lagged precipitation effects indicate soil moisture retention impacts future growing seasons.

Crop Vulnerability:

• Potatoes show the strongest negative temperature sensitivity, while wheat and maize demonstrate more climate resilience.

Conclusion

Policy Implications

1. Adaptive Farming: Encourage crop rotation strategies that account for 1-2 year climate lag effects

2. Irrigation Investment: Prioritize water management in regions showing precipitation declines

3. Breeding Programs: Focus on developing temperature-resilient varieties, especially for potatoes (since they aren’t very temperature resilient)

Limitations and Future Research

Limitations:

• TECHNOLOGY: There aren’t really accounting for technological improvements

• Major Weather: Excludes extreme weather events

Future directions:

• Incorporate monthly climate data

• Add soil quality and irrigation variables

• Analyze climate change scenario projections

This analysis demonstrates that climate variables indeed have significant lagged effects on agricultural productivity, with important variations across crop types. These findings can inform both short-term agricultural planning and long-term climate adaptation strategies. While not completely accurate, this analysis helps the reader and farmers understand the difference that planetary occurrences has on agricultural life.

For Fun Prediction (I tried)

Let’s Try some Prediction

set.seed(123)
filtered_data <- merged_data %>% filter(year >= 1990) %>% arrange(year)
n_rows <- nrow(filtered_data)
train_rows <- round(0.80 * n_rows)
train_data <- filtered_data %>% slice(1:train_rows)
test_data <- filtered_data %>% slice((train_rows + 1):n_rows)


model <- lm(Wheat_Yield ~ Temperature + Temp_Lag1 + Temp_Lag2 + Temp_Lag3 +
                                  Precipitation + Prec_Lag1 + Prec_Lag2 + Prec_Lag3, 
            data = train_data)


summary(model)

Call:
lm(formula = Wheat_Yield ~ Temperature + Temp_Lag1 + Temp_Lag2 + 
    Temp_Lag3 + Precipitation + Prec_Lag1 + Prec_Lag2 + Prec_Lag3, 
    data = train_data)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.7017 -0.7469 -0.3947  0.1829  2.6188 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)    1.992e+00  4.734e-01   4.207 5.64e-05 ***
Temperature    1.453e-01  3.196e-01   0.455    0.650    
Temp_Lag1      7.245e-02  3.425e-01   0.212    0.833    
Temp_Lag2     -7.057e-03  3.372e-01  -0.021    0.983    
Temp_Lag3     -2.165e-01  3.164e-01  -0.684    0.495    
Precipitation  1.068e-03  5.463e-03   0.195    0.845    
Prec_Lag1     -4.850e-04  5.529e-03  -0.088    0.930    
Prec_Lag2      7.082e-04  5.556e-03   0.127    0.899    
Prec_Lag3      7.149e-05  5.532e-03   0.013    0.990    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.137 on 100 degrees of freedom
Multiple R-squared:  0.0965,    Adjusted R-squared:  0.02422 
F-statistic: 1.335 on 8 and 100 DF,  p-value: 0.235

Predict on test data

predictions <- predict(model, newdata = test_data)


test_data$predictions <- predictions

Plot actual vs predicted values

ggplot(test_data) +
  geom_line(aes(x = year, y = Wheat_Yield, color = "Actual"), linewidth = 1) +
  geom_line(aes(x = year, y = predictions, color = "Predicted"), linewidth = 1) +
  scale_color_manual(values = c("Actual" = "blue", "Predicted" = "red")) +
  labs(title = "Actual vs Predicted Wheat Yield (Test Set)", x = "Year", y = "Wheat Yield (tons/ha)") +
  theme_minimal() +
  theme(legend.position = "bottom")

Calculate RMSE and MAE (Only One)

rmse <- sqrt(mean((test_data$Wheat_Yield - test_data$predictions)^2))
print(paste("RMSE: ", round(rmse, 2)))

[1] "RMSE:  1.44"

mae <- mean(abs(test_data$Wheat_Yield - test_data$predictions))
print(paste("MAE: ", round(mae, 2)))

[1] "MAE:  0.94"